Let A = 1, 2, 3, 4 , B = 4, 5, 6 , C = 5, 6 . Verify, A × (B ∩ C)… - Vidyadip

Question

Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Verify,

A × (B ∩ C) = (A × B) ∩ (A × C)

✓

Answer

A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}

(i) B ∩ C = {5, 6} A × (B ∩ C) = = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}

A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}

A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}

∴ (A × B) ∩ (A × C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}

∴ A × (B ∩ C) = (A × B) ∩ (A × C)

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